Sustainable Operation and Maintenance of Offshore Wind Farms Based on the Deep Wind Forecasting

Abstract

Offshore wind farms are becoming a pivotal solution to address the increasing energy demand worldwide and reduce carbon emissions to achieve a sustainable energy sector. Considering the higher operational and maintenance cost of offshore wind farms, it is important to make a good maintenance plan to guarantee the system’s reliability and reduce the total cost related to maintenance activities at the same time. Because maintenance planning is a long-term decision problem and the wind force is random, long-term wind force prediction is needed to help managers evaluate the loss caused by maintenances to be executed in the future. However, long-term wind force prediction is naturally complicated, which is much harder than the short-term (e.g., day-ahead) prediction widely investigated in the literature. In order to overcome this difficulty, we design a deep learning framework combining variational mode decomposition, a convolution neural network, long short-term memory network, and full-connected network. Using the public data from the city of Leeds, the prediction accuracy of the above framework is validated by comparing it with other prediction techniques. Then, the predicted wind force is input into the established optimization model determining preventive maintenances during a predefined period. Because the uncertainty of wind force is replaced by the prediction value, the optimization model can be established as a mixed-integer linear programing model, which only contains limited variables and can be solved quickly. Lastly, an abundance of numerical experiments are conducted to validate the effectiveness of the proposed optimization model, based on which some managerial insights are provided to the managers of offshore wind farms about the optimal operations and maintenance strategy. The research outcome will greatly promote the development of the wind power industry in the future.

1. Introduction

1.1. Background

The maturation of wind technology, economies of scale, and advances in turbine design are consistently driving down costs, rendering wind power increasingly competitive with traditional energy sources. Consequently, wind energy assumes a pivotal role in addressing global energy demands while mitigating carbon emissions, thereby promoting sustainability in the energy sector. In 2021, worldwide wind-generated renewable energy reached 1861.9 Terawatt-hours, boasting a remarkable 17% annual growth rate, as per data from the BP Statistical Review of World Energy [1]. This impressive growth trajectory is expected to persist, as an expanding number of countries, including China, invest in wind energy projects to fulfill their renewable energy and climate objectives [2].

Offshore locations typically offer a more dependable and potent wind resource than onshore sites, resulting in a more consistent and reliable energy output, thereby rendering offshore wind farms notably more efficient in electricity generation when compared to their land-based counterparts [3]. Moreover, offshore wind farms hold a distinct advantage as they do not encroach upon precious terrestrial real estate, preserving the potential for the multifaceted use of coastal areas and thereby presenting ample room for expansion. Furthermore, the expanse of offshore environments facilitates the deployment of larger and more robust wind turbines, unhindered by the spatial constraints often encountered on land. This capacity for utilizing larger turbines translates to heightened energy production per unit and ultimately reduces the total number of turbines required for a given capacity, consequently yielding substantial cost savings. The overall structure of offshore wind farms is shown in Figure 1.

While offshore wind farms offer numerous advantages, they are also accompanied by distinct challenges, including intricate installation requirements, heightened maintenance costs, and potential environmental and maritime concerns. Maintenance plays a crucial role in ensuring the sustained efficiency, safety, and profitability of these offshore installations. To facilitate effective maintenance planning, extensive research has delved into the failure modes of wind power generation system components. For instance, Li and Soares [4] employed Bayesian network analysis to scrutinize failure rates and the overall reliability of the offshore wind turbines. Such studies contribute to the development of robust maintenance strategies and underscore the essential nature of maintenance in optimizing offshore wind farm performance [5]. To uphold system reliability above a crucial threshold and minimize unexpected failures, the implementation of routine preventive maintenances (PMs) is imperative [6]. These PMs serve to inspect, identify, and rectify potential component failures. However, while increased PM frequency enhances reliability, it concurrently escalates maintenance costs and extends wind turbine downtime, subsequently diminishing system output. Furthermore, it is noteworthy that the timing of two equal-duration shutdowns can result in different output losses due to variations in wind forces during distinct periods [7].

To conclude, optimizing long-term preventive maintenance planning is essential to enhance the economic viability of offshore wind farms. It means that we need to ensure that maintenance activities are executed at optimal times, striking a balance between reliability enhancement and minimizing downtime-related productivity losses. These routine preventive maintenances, involving scheduled inspections and servicing, are indispensable for averting component degradation, encompassing vital elements such as turbine blades, gearboxes, and electrical systems in offshore wind farms. In addition, it is necessary to predict the wind force for the whole planning horizon when managers determine the maintenance plan because only accurate wind forecasting can lead to the accurate judgement of system output loss caused by the executed maintenances. However, the prediction of long-term wind force is rather difficult compared with the prediction of short-term wind force. That is also the reason why most articles about wind force prediction in the literature focus on the short-term prediction.

1.2. Motivations and Main Contributions

The published articles related to the maintenance management of offshore wind farms have indicated the difficulty caused by the unknown wind force when making the maintenance plan. Although researchers admit that this problem can be handled well if the unknown wind force can be predicted accurately, they still choose to use the stochastic model to deal with this difficulty because the long-term forecast of wind force is rather complicated. Therefore, the motivation of our paper is to build a prediction model using big data and deep learning methods to forecast the wind force during the whole period of maintenance planning, which can be used to simplify the optimization model of maintenance planning and obtain good application performance simultaneously.

Therefore, this paper aims to answer the following two research questions.

(1) What prediction techniques are suitable for long-term wind force forecasting? Addressing this question is crucial not only for optimizing maintenance planning within offshore wind farms but also for facilitating informed decision making across various operational aspects of wind farms. Additionally, research in this domain proves valuable when evaluating the potential profitability that long-term wind force forecasting can offer to offshore wind farms.

(2) How can an optimization model be developed to encapsulate the fundamental aspects of preventive maintenance in offshore wind farms while ensuring rapid solvability? Addressing this question is instrumental in assisting offshore wind farms in identifying efficient and cost-effective approaches to resolve their maintenance decision dilemmas.

In order to answer the first question, we design a large framework combining three different kinds of networks in Section 3. This can be viewed as the application of deep learning methods into the optimization area, which is a hot topic recently showing different research trends and advantages, such as Mocanu et al. [8] and Yang et al. [9]. Simultaneously, to demonstrate the efficacy of the devised framework, we utilize publicly available data from the city of Leeds to execute the entire process, subsequently comparing its performance against other conventional frameworks.

In order to answer the second question, we establish a mixed integer linear programming model in Section 2, which takes the wind force as one input parameter of model. This model is structured to define the objective function encompassing various cost components and constraints pertinent to practical maintenance requisites. Subsequently, numerical experiments, detailed in Section 4, are undertaken to validate the efficacy of this optimization model. Additionally, these experiments yield managerial insights gleaned from the numerical outcomes.

To sum up, the main contributions of this paper can be described as follows.

(1) A prediction model, combining the variational mode decomposition, convolutional neural network, long short-term memory network, and full-connected network, is designed to realize a good long-term wind force forecast. Not only can it be used in the maintenance optimization problem, but it can also be used in other applications.

(2) A mixed-integer linear programming model is established for the maintenance optimization problem, which considers different kinds of costs. The optimal solution can be solved by the common commercial solver such as Cplex, Gurobi, and COPT within an acceptable computation time.

(3) An abundance of numerical experiments are conducted in this paper. They not only validate the effectiveness of the prediction model and optimization model, but they also show the relationship between the total cost and different parameters, which can guide offshore wind farm managers to execute the most appropriate plan based on their reality.

1.3. Literature Review

In recent years, wind power has emerged as a significant contributor to the global power grid. With the development of renewable energy trading management platforms, the value utilization of renewable energy is also more convenient [10]. Its inherent cleanliness and environmental friendliness have propelled its rapid integration. Achieving the efficient utilization of wind energy necessitates the precise prediction of future wind speeds. Data collection for wind farms is becoming increasingly intensive. Kou et al. [11] summarized the data monitoring and operation and maintenance of offshore wind farms and explained the importance of wind farm data for wind turbine maintenance, and the future research directions in this field were explored. Studies on wind speed prediction can be categorized into short-term prediction and medium- to long-term prediction based on the length of their prediction time [12,13,14,15,16]. Jung et al. [17] summarized the knowledge of wind speed and power prediction and proposed methods to improve the prediction accuracy. Wang et al. [18] conducted a comprehensive summary and analysis of the wind speed prediction issue. They outlined the classification criteria for wind speed prediction, experimentally compared various prediction methods, and suggested that one-dimensional convolutional neural networks (CNNs) significantly enhance model prediction accuracy.

In the area of short-term forecasting, the available research studies are already mature and accurate. Shukur et al. [19] improved the machine learning Autoregressive Integrated Moving Average model (ARIMA) prediction method by combining an artificial neural network (ANN) with a Kalman Filter (KF) to construct a hybrid model for short-term wind speed prediction. Aasim et al. [20] used wavelet transform (WT) to decompose the data for prediction based on the ARIMA prediction method to achieve the ultra-short-term prediction of wind speed data. Liu et al. [21] applied a combination of long short-term memory neural networks (LSTMs) to the wind speed prediction problem. Liang et al. [22] used multivariate weather data to realize the prediction of wind speed based on an LSTM network. Liu et al. [23] proposed a hybrid prediction network, which decomposes the data and then applies multiple prediction models for separate predictions and finally realizes the prediction of wind speed together. Memarzadeh et al. [24] combined an LSTM model with algorithms such as the Crow Search Algorithm (CSA) and WT for wind speed prediction. Altan et al. [25] combined the LSTM network with the Gray Wolf Optimizer (GWO) decomposition method to create a new model to achieve the short-term single-step prediction of wind speed. Kim et al. [26] proposed a neural network prediction model combining CNN with LSTM and verified its effectiveness in a residential energy consumption prediction problem. Ghimire et al. [27] applied the combined CNN-LSTM model to the field of solar radiation prediction and verified the improvement of CNN convolution on the prediction accuracy of time series data.

In the area of medium- to long-term prediction forecasting, there have been some studies that have explored prediction methods and achieved wind speed data prediction over relatively long periods. Akash et al. [28] validated the accuracy of different machine learning prediction models at the long-period level. Liu et al. [29] provide an introduction to Variable Mode Decomposition (VMD) and propose a new signal decomposition method based on it in combination with Detrended Fluctuation Analysis (DFA). Han et al. [30] applied the VMD decomposition method to wind speed data decomposition and combined it with LSTM to realize the multi-step prediction of wind speed data. Liu et al. [31] used the wavelet decomposition method to process the data and combined it with a hybrid optimization framework for multi-step wind speed prediction. Zheng et al. [32] combined VMD with neural networks to realize the multi-step prediction of wind speed data. Wang et al. [33] considered the similarity characteristics of data between multiple sites to improve the multi-step wind speed prediction accuracy.

On the other side, the power generation systems of offshore wind farms consist of large and intricate wind turbines, facing challenges such as wear, degradation, and malfunctions within the wind power system. Ensuring the reliability, availability, maintainability, and safety of offshore wind power systems is paramount for their efficient and secure operation [34]. The selection of an appropriate maintenance strategy plays a pivotal role in the normal functioning of wind farms. Optimal maintenance strategies depend on various factors, including energy costs, required reliability levels, weather conditions, availability of skilled technical personnel, and the accessibility of crew transport vehicles [35,36,37]. Maintenance strategies may vary across different power plants based on factors such as the type, size, and number of wind turbines, required reliability, and other maintenance standards [38].

Extensive research has been conducted on the maintenance issues in production systems [39]. Common maintenance approaches include preventive maintenance (PM), corrective maintenance (CM), replacement maintenance (RM), and effective opportunity maintenance (OM), as well as predictive maintenance and condition-based maintenance [40,41]. Traditionally, maintenance methods have been predominantly passive, such as corrective maintenance, focusing on promptly addressing equipment or system failures to minimize downtime and production losses [42]. For instance, a mathematical model proposed by Nachimuthu et al. [43] aided stakeholders in offshore wind farms in making critical decisions related to corrective maintenance, considering uncertainties in turbine failure information.

With the advent of condition monitoring technologies, fault diagnostic techniques, and numerous fault control theories, the maintenance of wind power systems has witnessed significant advancements [44]. The offshore wind power industry is transitioning towards more proactive, state-based maintenance methods. Proactive strategies aim to take action before failures occur through regular, preventive, or prescriptive maintenance. Proactive maintenance primarily encompasses preventive maintenance and prescriptive maintenance, with the latter being an evolution of the former [45,46]. Both leverage operational data to determine the likelihood of wind turbine component failures, providing sufficient warnings for necessary maintenance [47]. Preventive maintenance reduces the probability of failures by conducting appropriate measurements before failures occur. It generally focuses on short-term planning, considering factors such as weather, personnel availability, and daily maintenance. Particularly challenging is the scheduling of maintenance work several days in advance due to the uncertainty of weather forecasts [48]. Tian and Zhang [49] researched component-level maintenance and economic dependencies, developing a predictive maintenance approach for wind farms. To address the fuzzy multi-objective decision-making problem of spare part batch size in long-term predictive maintenance planning for offshore wind farms, Su et al. [50] introduced a novel fuzzy multi-objective linear programming model, simultaneously evaluating maintenance costs and system reliability. The probability is calculated through Fault Tree Analysis and Binary Decision Diagrams to reduce computational costs. Garan et al. [51] utilized reinforcement learning methods, utilizing information provided by the system to optimize wind turbine operation and maintenance schedules. They compared it with common strategies such as predictive and planned maintenance, finding that the use of reinforcement learning methods results in higher average profits.

1.4. Theoretical Overviews

1.4.1. Variational Mode Decomposition (VMD)

Variational mode decomposition is an innovative data decomposition method employed for the analysis of non-stationary or nonlinear data. Compared with the rest of existing decomposition methods, this method can solve the problems of noise, sampling sensitivity, and other limitations, as the method is more robust to noise, and the detailed calculation process and principle can be found in the literature [52]. It effectively decomposes the original signal into many groups of sub-signals known as Intrinsic Mode Functions (IMFs). Each group of sub-signals possesses distinct local frequencies and modes, representing the long-term and local data characteristics of the original signal from low to high frequencies, respectively. Different from other decomposition models, VMD adopts a non-recursive solution method and can effectively extract the local characteristics of the data signal. It mainly consists of two parts: the construction and solution of variational problems. The VMD problem is formulated as an equation, where $u_k$ is the decomposition signal for each mode, $(\delta (t)+\frac{j}{\pi t})\cdot u_k\left(t\right)$ is the decomposition signal after the Hilbert transform calculation, $w_k$ is the center frequency, and $e^{-j{\omega }_{k}t}$ is the exponential term corresponding to the center frequency.

$$\left\{\begin{array}{c}\underset{\left\{u_k\right\},\left\{w_k\right\}}{min}\left\{{\displaystyle \sum _k}{‖{\partial }_t\left[\left(\delta (t)+\frac{j}{\pi t}\right)·u_k\left(t\right)\right]e^{-j{\omega }_{k}t}‖}^2\right\}\\ s.t. {\displaystyle \sum _k}{u}_k=f\end{array}\right.$$

First, the variation problem is constructed. Hilbert transform is performed on the original signal to obtain the analytical signal of $k$ modal components, and the single-sided spectrum is obtained. Then, the spectrum of each mode is modulated to the fundamental frequency band to complete the variation problem. The function construction is as shown in the formula, and then the function can be solved.

In the specific implementation, this paper employs the vmdpy open library in Python to implement the VMD function. For the determination of the decomposition dimension, i.e., the number of decompositions, of the raw wind speed data, the center frequency can be used for discrimination. After the decomposition of the original signal data, the center frequency of adjacent decomposition signals is compared, and if the relative value of the center frequency exceeds 90%, it is considered that the decomposition is excessive, and the maximum number of undecomposed excessive modes is selected as the target number for VMD [32]. In this paper, in order to simplify the data preprocessing steps, the VMD dimension of wind speed data in existing studies is used as the decomposition parameter. The number of decomposed modes, denoted as $K$, is set to 18, and the balance term $\alpha$ is assigned a value of 2000. This term serves to weigh the trade-off between the signal fitting and smoothness of the modal function.

In the prediction model construction of this paper, VMD is applied to the decomposition of raw mean wind speed data to solve the problem of the poor prediction effect of the original unstable signal. According to the existing studies on wind speed prediction, VMD can effectively deal with irregular wind speed data and combine with other models to obtain more accurate prediction results.

1.4.2. Convolutional Neural Networks (CNNs)

The convolutional neural network is a highly effective method for extracting data features, and it is a feed-forward neural network, commonly employed for the convolution and feature extraction of image data [53]. When dealing with time series data, CNNs can leverage one-dimensional convolution kernels to extract features from one-dimensional time series data. This approach contributes to enhancing the accuracy of deep learning prediction models. In the field of energy prediction, CNNs have been used in many applications and have shown great advantages. For example, solar radiation prediction has verified its powerful role in neural network prediction [27]. Its main role is in the characteristics of complex time series data. The extraction helps other prediction models such as recurrent neural network (RNN) models to extract features from complex time series data.

This study uses a one-dimensional convolutional neural network (1-D CNN), which conducts data convolution for feature extraction on one-dimensional time series wind speed data. The CNN performs sliding convolution on one-dimensional data based on the size of the convolution kernel and superposes the data around a single data point to generate new convolutional values, effectively achieving convolution on data features.

$$h_{ij}=f\left(X_i·w_j+b\right)$$

The process is depicted in the formula, where $h_{ij}$ represents the new value after convolution, $f$ is the activation function, $X_i$ denotes the data sequence of the input convolution kernel, $w_j$ represents the weight information of the convolution kernel, and $b$ is the bias term. In this study, the Rectified Linear Unit (ReLU) function was employed as the activation function, and the Adam optimizer was utilized.

In the prediction model construction of this paper, the convolutional neural network was used to construct the data feature extraction layer, which utilizes its efficient extraction capability of data features to achieve feature extraction of one-dimensional average wind speed data. The convolutional layer will help the subsequent neural network to carry out deep feature learning and improve the prediction accuracy.

1.4.3. Long Short-Term Memory Network (LSTM)

The long short-term memory neural network is an evolution of the RNN, designed for predicting long-term cyclic time series data.

RNN is different from CNN in that its elements are not independent of each other. The LSTM model increases the connectivity between elements, that is, the inheritance of information is increased between elements. Similar to other recurrent neural network structures, a set of neural network loops in the RNN model can be expanded into a process in which multiple nodes are processed individually and passed to each other. Each node consists of three layers, namely, the input layer, hidden layer, and output layer. During the processing of each node, the neurons receive information from both the input layer and the hidden layer of the preceding node, producing the output result. However, when the time series data are excessively long, the information from the hidden layer of the preceding nodes that the current node can receive gradually diminishes. This leads to a diminishing impact of the preceding node information, resulting in the loss of data features from preceding nodes in the input information to the neuron. This contributes to suboptimal performance in predicting long-term cyclic time series.

The LSTM model is developed from the RNN model to address the issue of gradient vanishing of the preceding node’s information in long sequences that occurs in the RNN model. The difference is also the core of the LSTM model, which always runs through the entire recurrent neural network and is used for information transfer between nodes when predicting long-term series data.

Compared with the RNN model, the LSTM model adds a new gate control mechanism, which realizes the memory and forgetting of information in the neural network by controlling the increase and decrease in information in the network. The problem of data feature loss in RNN networks during the prediction of too long time series data can be solved by adding a forgetting gate [54]. A singular LSTM recurrent structure comprises three gates processed sequentially: the forget gate, input gate, and output gate. The forget gate receives data from the previous time step and data features from the current time step. It processes the input information through neurons activated by the sigmoid function, yielding a ratio value that determines the extent to which information from the previous time step is retained. In summary, the LSTM model achieves the long-term transmission of information in long sequence loop problems by adding a gate control mechanism and a cell state layer, effectively solving the problem of the inability of the long-term transmission of information in the RNN model.

In the prediction model construction of this paper, LSTM constitutes the prediction layer of the entire neural network. The LSTM network achieves the purpose of learning the features of the post-convolution data and realizing the final prediction.

2. Problem Description

Before describing the problem characteristics, the notations used in modeling and methodology are shown in

Table 1. Notation in the maintenance planning model.

Notation	Definition
$T$	Set of periods; indexed by $t\in T$
$I$	Set of wind turbines; indexed by $i\in I$
$q_t$	Predicted wind force at period $t$
$r_t$	Equals 1 when condition is allowed to conduct PM; 0, otherwise
$l$	Maximum length of time interval between two consecutive PMs
$h$	Length of execution time for one PM
$m$	Maximum number of concurrently maintained wind turbines
$p$	Penalty cost per unit of lost wind force
$u$	PM cost of one wind turbine
$v$	Operations cost of one vessel during a single service
$H$	A very large constant
$x_{it}$	Binary variable; it equals 1 if one PM of turbine $i$ is started at $t$
$y_{it}$	Binary variable; it equals 1 if one PM of turbine $i$ is conducted at $t$
$z_t$	Binary variable; it equals 1 if one vessel is set up at period $t$
$s_{it}$	Continuous variable; it is denoted as the continual working time of turbine $i$ at period $t$ since the last conducted PM

and

Table 2. Notation in the wind force prediction model.

Notation	Definition
ACF	The autocorrelation function
ReLU	The activation function of CNN and LSTM
${IMF}_n$	The signal after VMD of group $n$
$Q_{\mathrm{normalized}}$	The data after data standardization
$Q_{\mathrm{o}\mathrm{b}\mathrm{s}\mathrm{e}\mathrm{r}\mathrm{v}\mathrm{e}\mathrm{d}}$	The daily average wind speed data
$Q_{\max }$	$\mathrm{The} \mathrm{maximum} \mathrm{value} \mathrm{of} Q_{\mathrm{o}\mathrm{b}\mathrm{s}\mathrm{e}\mathrm{r}\mathrm{v}\mathrm{e}\mathrm{d}}$
$Q_{\min }$	$\mathrm{The} \mathrm{minimum} \mathrm{value} \mathrm{of} Q_{\mathrm{o}\mathrm{b}\mathrm{s}\mathrm{e}\mathrm{r}\mathrm{v}\mathrm{e}\mathrm{d}}$
$Q_t$	The true value of daily average wind speed at period $t$

. In Table 1, the problem parameters and decision variables of the optimization model formulating maintenance planning are defined. Particularly, the parameter $q_t$ is the corresponding predicted value of $Q_t$, which is defined in Table 2. In Table 2, the notations used to describe the process predicting long-term wind force are defined. Because the content of the prediction model is rather long, we put them in Section 3.

2.1. Maintenance Problem Formulation

Offshore wind power has emerged as a pivotal frontier in wind energy generation. The shift towards expansive wind farms located in coastal waters is attributed to the abundance of ocean wind energy, minimal land footprint, and fewer environmental constraints. Typically situated around 10 km off the coast on the continental shelf at depths of approximately 10 m, offshore wind farms comprise multiple wind turbines affixed to offshore supports, forming extensive arrays. These turbines are upheld by diverse structural frameworks such as offshore platforms, pilings, and floating supports, ensuring stability and reliability in marine conditions. The electricity generated in offshore wind farms is predominantly in the form of alternating current (AC). Yet, for efficient power transmission to the mainland, the AC power from offshore stations is commonly converted to direct current (DC) through converters. These factors contribute to high costs, with land costs being double or triple. Offshore wind farms provide an important contribution to the utilization of renewable energy sources, helping to reduce greenhouse gas emissions. However, because the offshore wind farm environment is harsh and complex, the equipment fault rate of offshore wind farms is significantly higher than that of onshore wind farms. Meanwhile, the operation and maintenance cost of offshore wind farms is much higher than that of onshore wind farms. Traditional operation and maintenance methods are not enough to meet the operation and maintenance requirements of offshore wind farms. Therefore, it is of great importance to establish a reasonable operation and maintenance management scheme for the stable development of offshore wind farms. Preventive maintenance will play an important role in the management of offshore wind farms and also represent the future development direction of offshore wind power operation and maintenance strategies.

PMs are meant to prevent failures and prolong the lifetime of wind turbines, which are determined by the decision maker beforehand. To perform these maintenance activities, a maintenance service provider (MSP) is needed. The MSP is a third party providing the maintenance service and required resources, such as vessels and technicians. We consider only one given MSP that is deployed for performing maintenance tasks and travels by vessel to the offshore wind farm. Whenever an offshore wind farm needs to conduct PM, the MSP can arrive and start maintenance immediately. In offshore wind farms, the wind conditions can be complex and dynamic due to the open-sea environment. The accurate prediction of wind conditions is crucial for making a great maintenance plan. Deep learning methods are employed for wind force prediction in offshore wind farms due to their ability to capture intricate patterns and relationships within large and complex datasets. This enables decision makers to make informed decisions regarding energy production and wind turbine maintenance, ultimately enhancing the overall efficiency and reliability of offshore wind energy generation.

There are some costs involved in operation and maintenance, including the PM cost, the vessel cost, and the penalty cost caused by the loss of wind force. The MSP maintains operations by charging for the provided service and resources. Therefore, there is an associated operating cost $v$ with one vessel during a single service. The MSP with one vessel can maintain up to $m$ wind turbines at the same time, and every wind turbine has an operator to manage operations and maintenance. It costs $u$ to conduct PM for one wind turbine. Furthermore, when wind turbines are being maintained, the devices must be shut down. In this case, electricity cannot be generated. Therefore, it is necessary to bear the penalty cost per unit of lost wind force $p$ during the execution of maintenance tasks.

This study aims to make a great maintenance plan to concurrently reduce the total cost related to the maintenance activities and guarantee the wind turbines’ reliability based on the forecast wind force. To achieve this, we develop a mixed-integer linear programming model to formulate the objective function related to different kinds of cost and the constraints related to the practical maintenance requirements. To enhance the efficient operation of offshore wind farms, we discuss the operation issue of an offshore wind farm that can be described as an optimization problem consisting of determining the ideal electricity production and maintenance strategies. It is related to a maintenance team and maintenance activities that are supported at an offshore wind farm consisting of several wind turbines during a predefined scheduling period $T$. The reliability of a set of wind turbines $I$ needs to be evaluated in each planning period. When the continual working time of each wind turbine $i$ ($i\in I$) is about to exceed the maximum length of time interval $l$ between two consecutive PMs, wind turbines might be shut down to conduct maintenance. In the following, we present the optimization model for the PM planning.

2.2. Mathematical Modeling

The mathematical model can be established as follows.

$$Min {\sum }_{t\in T}{\sum }_{i\in I}u{x}_{it}+{\sum }_{t\in T}v{z}_t+{\sum }_{t\in T}{\sum }_{i\in I}p{q}_t{y}_{it}$$

$$S.t., {\sum }_{i\in I}{x}_{it}\le m \forall t$$

(1)

$$y_{it}\ge x_{i{t}^{\prime }} \forall \mathrm{m}\mathrm{a}\mathrm{x}(t-h,1)\le t^{\prime }\le t, \forall i,\forall t$$

(2)

$$x_{it}\ge y_{it}-y_{i,t-1}\hspace{1em}\forall i,\forall t\ge 2$$

(3)

$$x_{i1}\ge y_{i1}$$

(4)

$$y_{it}\le r_t\hspace{1em}\forall i,\forall t$$

(5)

$$z_t\ge x_{it}\hspace{1em}\forall i,\forall t$$

(6)

$$x_{it}\le 0\hspace{1em}\forall i,\forall t\ge \left|T\right|-h+1$$

(7)

$$s_{it}\le s_{i,t-1}+1 \forall i,\forall t\ge 2$$

(8)

$$s_{it}\ge s_{i,t-1}+1-H{y}_{it} \forall i,\forall t\ge 2$$

(9)

$$s_{it}\le H\left(1-y_{it}\right) \forall i,\forall t$$

(10)

$$s_{it}\le l \forall i,\forall t$$

(11)

$$x_{it},y_{it},z_t \mathrm{are} \mathrm{binaries}; s_{it}\ge 0$$

(12)

The objective function includes three parts: the PM cost, the vessel cost, and the penalty cost caused by the loss of wind force. Constraint (1) specifies the maintenance crew capacity limit, which ensures that the PMs started concurrently cannot be larger than $m$. Constraints (2)–(4) specify that once a PM is started at period $t$, then the PM will be conducted for a time length of $h$. Constraint (5) ensures that the PM cannot be conducted in those periods with bad weather conditions. Constraint (6) requires that any one PM for any wind turbine must be supplied by a maintenance vessel. Constraint (7) means that any conducted PM must be finished before the end period $\left|T\right|$. Constraints (8)–(10) calculate the continual working time of the wind turbine at each period; the continual working time of the wind turbine will be set to 0 when a PM is conducted in one period. Constraint (11) ensures that the maximum continual working time will be obeyed, which guarantees the reliability of the system. Constraint (12) specifies the domains of decision variables.

3. Wind Forecasting Procedure

In this section, a deep learning method is designed to forecast a long-term wind force $q_t, \forall t\in T$, which is an important input parameter of the above maintenance problem model. It is obvious that a more accurate forecast of this parameter will lead to a better optimization result because it gives a better evaluation of wind loss.

3.1. Data Preprocess

The dataset used in this study is the public meteorological dataset on the Data Mill North website (https://datamillnorth.org/dataset/e1djp/leeds-meteorological-data, accessed on 1 November 2023). This website is a collaborative website originally set up by Leeds City Council. The open data website established by Leeds City Council provides data from various departments in the city to help people propose innovative solutions and solve urban problems. This dataset comes from the meteorological data recorded by the Knowsthorpe Gate (Long: −1.543237, Lat: 53.787769) weather station in Leeds, including 1 h and 15 min resolution data. In this paper, we take the Leeds city site data as an example to construct and validate the effectiveness of the predictive model, and the constructed model is generalizable. For other sites, different datasets can be used to train the same model structure.

The meteorological dataset used in this study spans from 1 January 2000 to 1 July 2018, with a one-hour resolution. In total, there are 166,559 records, covering various fields such as wind direction, wind speed, temperature, global radiation, and relative humidity. This study only uses wind speed data for time series forecasting, and the unit of wind speed data is $\mathrm{m}/\mathrm{s}$.

This study needs to optimize the wind turbine maintenance plan based on the wind speed prediction results in the future period, and its basis is data in the daily time dimension. To this end, for the existing wind speed meteorological data with a resolution of 1 h, the daily average wind speed is used as an indicator, and the data dimension is converted into the daily dimension by averaging the wind speed data recorded for 24 h a day to represent the wind speed characteristics of that day.

In the basic dataset, wind speeds from 2000 to 2017 were mostly between 2 m/s and 10 m/s. For this reason, there is an abnormal risk in data that deviate too much from this range. In 2018, some recorded values were as high as about 300 m/s. It deviates from the data of previous years and the reasonable range of wind speed. To prevent misleading data for this study, the data from 2018 were eliminated, and only the data from 2000 to 2017 were retained as research data to implement the steps of processing outliers in the dataset. Due to equipment failure, daily maintenance, and other reasons, wind speed data records will be missing. In order to ensure the continuity of data to the greatest extent, this study uses the average data of the same dates in other years as the filling of data nulls to complete the processing of missing values. The processed and transformed data are shown in Figure 2.

Through the stationarity test of the data, the data meet the stationarity requirements in the time series, but the data noise is too large and it is impossible to achieve a high degree of extraction of data trends and features. Therefore, VMD is applied to the data, and the daily average wind speed data are decomposed into 18 groups of component data. It is used to extract data trends and features, as shown in Figure 3.

3.2. Design of the Prediction Model

In this study, the prediction model and baseline model are constructed using Python 3.9.2 and deep learning libraries such as Keras 2.11.0, TensorFlow 2.11.0, and scikit-learn 1.2.2. The main objective is to build a VMD-CLSTM model by incorporating VMD, CNN, and LSTM neural networks. The goal is to achieve accurate predictions for long-term wind speeds over the next 60 days, providing a data foundation for wind turbine maintenance models.

To illustrate the process of model building, we first need to create a dataset for training and validation. For model training data, we will use the max-min normalization method to standardize the input data and scale it to the range [0, 1] to improve the efficiency of model training and prediction. The normalization and denormalization process is shown in the following equation, where $Q_{\mathrm{o}\mathrm{b}\mathrm{s}\mathrm{e}\mathrm{r}\mathrm{v}\mathrm{e}\mathrm{d}}$ is the un-normalized data, $Q_{\mathrm{normalized}}$ is the normalized data, $Q_{\max }$ is the maximum value in the set of data, and $Q_{\min }$ is the minimum value in the set of data.

$$\begin{gathered} Q_{\mathrm{normalized}}=\frac{Q_{\mathrm{o}\mathrm{b}\mathrm{s}\mathrm{e}\mathrm{r}\mathrm{v}\mathrm{e}\mathrm{d}}-Q_{\min }}{Q_{\max }-Q_{\min }} \\ {Q}_{\mathrm{o}\mathrm{b}\mathrm{s}\mathrm{e}\mathrm{r}\mathrm{v}\mathrm{e}\mathrm{d}}=Q_{\mathrm{normalized}}·(Q_{\max }-Q_{\min })+Q_{\min } \end{gathered}$$

In the process of generating the dataset required for the model, this study used the last 60 days of data as the test set and the remaining data as the training set.

ACF correlation analysis is a common method for determining the historical data step size required for the model in the deep learning prediction process [27], which calculates the degree of correlation between the current data and the historical data by performing a correlation analysis on the time series data used. Then, in combination with the actual situation, the historical data with a strong correlation are selected as the historical step size for model training to achieve better training results. During the training set data processing process, through ACF correlation analysis of the data and combined with actual experience, 50 was selected as the lag value, that is, using $(t-50, t-49,\dots ,t)$ time data to predict $t+1$. The daily average wind speed is used as input data, and the iterative loop is used to predict the 60-day long-term data.

The overall structure of the VMD-CLSTM model is shown in Figure 4. The input data are decomposed into 18 groups of data components through VMD, as shown in Figure 3, respectively named ${IMF}_n$, where $n$ represents the component serial number. CNN-LSTM models were constructed and trained on the 18 groups of decomposed data. By integrating the predicted output values of each group of models, the predicted value of wind speed was obtained. The predicted value is reused as the input data of the model for prediction, and repeated iterations can achieve the prediction results of wind speed data for the next 60 days for a long period.

In this paper, the construction of the wind farm has been completed. The purpose of the study is to optimize the maintenance program of the wind farm within 60 days. The dataset used is the historical data for a total of 17 years from 2001 to 2017, and the long-term prediction of the average wind speed in the next 60 days is achieved by a deep learning network based on the learning trend of the historical wind speed data. The historical data are fitted for the training to predict the average wind speed in the next 60 days. Due to the difficulty of the accurate prediction of long-term wind speed, the 60-day time period in the field of prediction already belongs to a long prediction period.

As shown in Figure 5, the CLSTM model consists of several components: the input layer, convolutional layers, prediction layer, and output layer, as depicted in the diagram. The convolutional layers comprise three CNN convolutional layers, one pooling layer, and one flattening layer. The prediction layer incorporates an LSTM neural network. Notably, compared to conventional convolutional neural networks, the first three layers of the convolutional network (the three CNN convolutional layers) use 1-D convolution for extracting temporal features from time series data. The post-convolution data undergo pooling in the pooling layer to prevent overfitting. The output data from the flattening layer serve as input to the LSTM layer, facilitating the prediction of average wind speed for the next day based on feature information. The CLSTM model uses mean squared error (MSE) as the evaluation metric during the training process. In the VMD-CLSTM model, the CLSTM model is employed for predicting each data component obtained after VMD. The predictions for each component are then combined to achieve the forecast of average wind speed for the next day.

This study conducts comparative experiments using baseline models to validate the predictive superiority of the VMD-CLSTM model. The baseline models include the CLSTM model and the VMD-LSTM model. Specifically, the CLSTM model directly predicts daily average wind speed data without VMD, serving as a comparison to investigate the impact of VMD in the VMD-CLSTM model. The VMD-LSTM model exclusively employs the LSTM model for prediction without utilizing VMD on the data previously decomposed by VMD, providing a comparison to explore the role of CNN convolution in feature extraction. Through a search for model hyperparameters, the parameters employed in this study for each model are outlined in

Table 3. Parameters for different models.

Parameters	CLSTM	VMD-CLSTM	VMD-CLSTM
VMD targets	-	18	18
CNN Layer1(C1)	90	90	-
CNN Layer2(C1)	20	20	-
CNN Layer3(C1)	50	50	-
CNN Activation function	RELU	RELU	-
Pooling Size	2	2	-
LSTM Layer(L1)	128	128	128
LSTM Activation function	RELU	RELU	RELU
Batch size	600	600	600
Learning rate	0.001	0.001	0.001
Regularizer	l2 (0.01)	l2 (0.01)	l2 (0.01)
Epochs	100	50	200

.

3.3. Prediction Performance Criteria

To assess the predictive performance of the proposed forecasting model and baseline models in this study, the mean absolute error (MAE), mean absolute percentage error (MAPE), and root mean squared error (RMSE) are employed as evaluation metrics for forecasting accuracy.

(1) MAE (Mean Absolute Error)

MAE refers to the average degree of deviation between the model predicted value and the sample true value. Compared with MSE, MAE has a certain tolerance for discrete points, that is, it is less sensitive to discrete points. At the same time, in MSE, the degree of deviation is calculated through the absolute value, so the punishment for the deviation values on different sides is consistent, there is no problem of mutual cancellation, and the degree of data deviation can be completely reflected. On the same dataset, for the prediction results of different models, the smaller the MAE value, the better the prediction effect, and vice versa. The calculation process is shown in the following equation, where $Q_t$ is the true value and $q_t$ is the predicted value at period $t$.

$$\mathrm{MAE}=\frac{1}{\left|T\right|}\sum _{t\in T}\left|q_t-Q_t\right|$$

(2) RMSE (Root Mean Squared Error)

RMSE, root mean squared error, is a data prediction accuracy test indicator. By calculating the square root of the deviation between the predicted value and the true value and the square root of the ratio of the number of observations, the degree of deviation between the predicted value and the true value is obtained. In the prediction results of different models, the smaller the RMSE value, the better the prediction effect, and vice versa. The calculation process is shown in the following equation.

$$\mathrm{RMSE}=\sqrt{\frac{1}{\left|T\right|}\sum _{t\in T}(q_t-Q_t{)}^2}$$

(3) MAPE (Mean Absolute Percentage Error)

MAPE, mean absolute percentage error, is a calculation index of relative error, which reflects the accuracy of prediction by calculating the deviation of the predicted value from the true value. Compared with MAE and RMSE, MAPE uses absolute values for calculation to avoid the mutual cancellation of error values in different directions. At the same time, it uses relative error calculation methods to make calculation indicators directly comparable across different data and models. For different models, the smaller the MAPE value, the smaller the relative deviation of the model’s prediction results, the better the prediction effect, and the worse the prediction effect. The calculation process is shown in the following equation.

$$\mathrm{MAPE}=\frac{1}{\left|T\right|}\sum _{t\in T}\left|\frac{Q_t-q_t}{Q_t}\right|$$

3.4. Prediction Results

To validate the effectiveness of the VMD-CLSTM model constructed in this study for long-term daily average wind speed prediction, the aforementioned model parameters and structures were utilized to build the prediction model VMD-CLSTM, along with baseline models. Comparative experiments were conducted on real datasets using a test set containing typical wind speed data for a 60-day period. The experimental results are depicted in Figure 6, and the error assessments for each model are presented in

Table 4. Error indicators for prediction results of different models.

Error Indicator	CLSTM	VMD-LSTM	VMD-CLSTM
MAE	1.1485	1.0156	0.9482
RMSE	1.4498	1.2509	1.1725
MAPE	33.3949%	32.8897%	32.3132%

.

It is obvious from the prediction images that in the prediction results of the test set, the CLSTM model, which does not use VMD for data decomposition processing, causes the neural network temporal prediction model, LSTM, to be unable to effectively accomplish the prediction task for wind speed data over long periods of time due to the high fluctuation of the wind speed data, even in the case of CNN for data feature extraction. After several cycles of prediction, the predicted value of the model tends to flatten out, losing the temporal trend of the wind speed data over a long period of time, and the generated prediction data cannot be used for the optimization solution of the subsequent wind turbine maintenance model. After using VMD to decompose the data, the deep learning model LSTM model can maintain the fitting of the long-term trend of the data in the long-period time series prediction, but the single LSTM model has a weak ability to extract the data features, and although it realizes the fitting of the trend of the features of the data over a long period of time to a certain extent, the degree of fitting is poor, which affects the accuracy of the model prediction. In the VMD-CLSTM prediction image, on the basis of the VMD-LSTM model, three CNN convolutional layers are added to increase the data feature extraction ability of the model, and it can be seen from the prediction result image that the VMD-CLSTM model is more prominent in its feature fitting ability in the wind speed long-period prediction problem and the prediction is more accurate, compared to the VMD-LSTM model.

In Table 4, the quantitative evaluation of each model prediction result is accomplished by displaying the prediction result error on the test set using the three metrics of MAE, RMSE, and MAPE. Combined with the prediction images of each model, the single CLSTM model is unable to complete the prediction of long-period wind speed data, and it loses data features and causes large prediction errors in the cyclic prediction process. After the VMD, the prediction errors of the CLSTM model using CNN for data feature extraction are better than the LSTM neural network without CNN, and the fitting of data features is more thorough. Therefore, the VMD-CLSTM model constructed in this paper has obvious superiority in the process of complex long-period wind speed data prediction, which is selected to predict the wind speed as a source of data required for turbine maintenance model optimization.

The reasons why VMD-CLSTM is applicable to the problem of long-term wind speed prediction mainly include the following: (1) The average wind speed time series data are irregular, without data feature extraction preprocessing (data decomposition), so when the prediction model is directly used for prediction, it cannot accurately fit the trend of the data, and it will result in the loss of the long-term trend, which makes it impossible to realize accurate prediction. Using VMD to decompose the data, the signals of different frequencies of the data can be predicted separately, which ensures the effective learning of data features in the long-term prediction process and can realize the fitting of the data trend in the long-term range. (2) Using CNN to extract features from each decomposed signal improves the model’s ability to extract features from the data, and relative to direct time series prediction, CNN is able to extract more data features, making the prediction structure more accurate. (3) The LSTM model is an efficient model for time series prediction, which has demonstrated its unique superiority in many time series prediction problems, i.e., the effective retention of the long-term trend of the data.

Through the above content, this study constructed a prediction model and was able to realize the long-term prediction of wind speed data for the next 60 days. However, due to the weak regularity of the wind speed data in the time series, it is difficult to make long-term predictions with high accuracy, the existing studies on wind speed prediction have only realized the prediction of wind speed data for the next week (7 days) at most, and the prediction accuracy is lower with the passage of time. For this reason, the prediction model constructed in this paper, to a certain extent, achieves the purpose of long-term prediction and can meet the needs of the subsequent scheduling optimization model. However, the prediction accuracy is relatively low for the prediction, which is limited by the amount of data and computing power, and only deals with one-dimensional time series data of average wind speed. In the future, when the arithmetic power allows, more complex algorithms can be further designed to construct a multivariate prediction model based on the multisite wind speed data and combined with the rest of the variables, such as temperature, barometric pressure, weather, and other data, so as to input the multidimensional data into the model, improve the model prediction accuracy, and reduce the prediction error. Due to the efficient processing capability of the neural network model for multidimensional data, the model structure is still applicable. And, when dealing with different dimensional data, it is sufficient to modify the data input dimension and convolution dimension. Thus, there is no dimensional disaster. Also, future improvements can be made from the perspective of predictive modeling by using more advanced predictive models, such as combining neural networks with stochastic differential equations to reduce the prediction error [55,56].

4. Numerical Analysis

Because the optimization model constructed in this paper is relatively simple, Gurobi will be directly applied to solve the mixed-integer linear programming model. Numerical validation is carried out using Python 3.9.7 in a simulation environment of a portable computer with an Intel i5-9300H CPU at 2.4 GHz.

4.1. Value of Wind Forecasting

To validate whether the predicted wind power can effectively describe the future variation trend of offshore wind power over a certain period, this study will comparatively analyze the total maintenance costs under actual wind conditions, under predicted wind conditions, under the average wind speed of the past 60 days, and under the actual wind conditions of the past 60 days. The case parameters are as follows: a period of 60 days; an offshore wind farm with 30 turbines; a two-day duration for performing PM; a maximum time interval of 15 days between consecutive PMs; a maximum capacity of 30 turbines that can be simultaneously maintained by one vessel, with an operating cost of USD 3000 per service; a PM cost of USD 200 per turbine; and a penalty cost of USD 100 per unit loss of wind power. This set of parameters is defined as configuration A, representing a common scenario for subsequent experiments. Consequently, 10 sets of results under different time intervals were obtained (

Table 5. Maintenance costs for each maintenance program at different time intervals.

I	Case	Period	Real		Prediction		Average		Real Past
			Value/USD	Time/s	Value/USD	Time/s	Value/USD	Time/s	Value/USD	Time/s
30	1	2 November 2017–31 December 2017	92,430	8.43	121,470	15.16	126,332	17.04	130,859	16.17
	2	3 September 2017–1 November 2017	96,095	2.21	104,240	3.13	123,778	16.96	132,918	3.30
	3	5 July 2017–2 September 2017	110,969	2.88	126,646	2.45	136,123	7.29	128,517	2.27
	4	6 May 2017–4 July 2017	83,683	2.31	142,877	16.64	135,001	8.56	125,983	5.78
	5	7 March 2017–5 May 2017	103,951	17.20	111,686	18.08	118,432	13.45	113,890	10.12
	6	6 January 2017–6 March 2017	86,012	4.74	129,661	2.44	106,928	12.20	123,275	18.49
	7	7 November 2016–5 January 2017	77,389	8.63	93,347	7.85	118,105	19.01	141,894	11.77
	8	8 September 2016–6 November 2016	90,113	15.34	104,921	13.47	111,678	8.60	111,269	4.32
	9	10 July 2016–7 September 2016	103,284	3.50	129,396	8.68	149,478	2.03	124,261	10.66
	10	11 May 2016–9 July 2016	83,424	2.27	96,855	9.22	99,057	7.72	98,453	8.19
	Mean	-	92,735	-	116,110	-	122,491	-	123,132	-
	Gap	-	-	-	25.21%	-	32.09%	-	32.78%	-

).

In the above table, $Gap=\frac{Costs under other winds - The cost under real wind}{The cost under real wind}$. As can be seen in Table 5, the difference between the total cost of the maintenance program under the predicted wind and the total cost of the maintenance program under the actual wind for each case is usually small. In contrast, the difference between the total cost of the maintenance program under the average of the last 60 days of actual wind, the total cost of the maintenance program under the last 60 days of actual wind, and the total cost of the maintenance program under actual wind is more significant. And this is satisfied in 7 out of 10 sets of examples, thus proving the validity of the wind prediction. In very few cases in the above examples, the total cost of the maintenance program under the predicted wind is slightly larger than the total cost of the maintenance program under the average of the true wind for the last 60 days and the total cost of the maintenance program under the actual wind for the last 60 days. This is due to the large fluctuations in wind on some days, resulting in a large deviation between the predicted wind and the actual wind. Even if the accuracy of the forecast data is high, if the peaks and troughs of the forecast data fail to match the actual data, it may lead to poor forecasting.

To further verify the validity of wind prediction, the case under different wind turbine numbers is considered in this paper. We sequentially utilize 10 sets of wind power data for different time intervals under wind turbine numbers of {10, 20, 30, 40, 50} for the calculations, and then we obtain the average value of each set under different maintenance plans (

Table 6. Mean value and gap of maintenance cost for each maintenance program with a different number of wind turbines.

I	Real	Prediction		Average		Real Past
	Mean	Mean	Gap	Mean	Gap	Mean	Gap
10	36,912	44,703	21.11%	46,830	26.87%	47,044	27.45%
15	50,868	62,555	22.98%	65,746	29.25%	66,066	29.88%
20	64,823	80,407	24.04%	84,661	30.60%	85,088	31.26%
25	78,779	98,258	24.73%	103,576	31.48%	104,110	32.15%
30	92,735	116,110	25.21%	122,491	32.09%	123,132	32.78%

). It can be seen from the table that for each case, the difference between the total cost of the maintenance program under the predicted winds and the total cost of the maintenance program under the actual winds is usually small. In contrast, the difference between the total cost of the other two groups and the total cost of the maintenance program under actual wind is more significant.

First of all, the maintenance program under predicted wind is able to make a more accurate prediction of future wind conditions based on information such as historical data and weather forecasts. This allows managers to schedule maintenance in advance, avoiding additional repair costs due to unexpected strong winds. In contrast, maintenance schedules based on wind data and averages over the past 60 days are often unable to respond to wind changes in a timely manner. This may require temporary adjustments to the maintenance plan, which increases the waste of labor and material resources. Secondly, the maintenance plan under predicted wind is also able to optimize and adjust the maintenance work according to the wind trend. For example, maintenance is performed on wind turbines in low-wind conditions to minimize the cost of losses due to wind turbine downtime, while no maintenance is performed on wind turbines in high-wind conditions to improve the efficiency of wind power generation. This flexible adjustment strategy allows for the total maintenance cost to be effectively controlled. In addition, the maintenance program under the predicted wind power can also improve the reliability and stability of the equipment. By accurately predicting wind variations, maintenance personnel can identify potential problems in advance and take appropriate preventive measures to avoid equipment failures under adverse wind conditions. This not only reduces maintenance costs but also improves the operational efficiency and service life of the equipment.

In summary, this result fully illustrates the importance of wind prediction for reducing maintenance costs and improving equipment reliability and stability. Therefore, managers should pay more attention to the application of wind prediction in future maintenance work in order to realize the more efficient and economical maintenance management of offshore wind farms.

4.2. Effectiveness of Optimization Model

To verify the effectiveness of the proposed mixed-integer linear programming model, this section formulates a manual scheduling rule based on the actual situation in the maintenance process. Specifically, a vessel is dispatched to the offshore wind farm for wind turbine maintenance on the first day of the maintenance cycle, and a vessel is dispatched again if there are still unmaintained turbines during the maintenance process of the first vessel. The time interval of the maintenance schedule depends exactly on the maximum time interval between two adjacent PMs. In this way, the maintenance schedule is automatically scheduled through this manual scheduling rule. We considered wind forecast data for the 600 days from 11 May 2016 to 31 December 2017 and divided them into 10 cases by time interval. The length of each time interval is 60 days. The wind turbines need to be maintained at least once every 15 days. Therefore, several maintenance tasks need to be performed in a time interval. The optimal maintenance schedules for each case and their corresponding maintenance costs are obtained through the proposed model. Then, the maintenance cost of each case under the maintenance plan generated by the manual scheduling rule is calculated and the results of each case are compared with the results of the optimization model. By utilizing parameter configuration A, the results shown in Figure 7 are obtained.

Figure 7 illustrates a discernible trend indicating that the total expenditure on maintenance schedules, derived from the optimization model, is comparatively low within each case. This result has a significant advantage over the maintenance plan under manual scheduling. By rationally allocating maintenance personnel and equipment resources, the optimization model can avoid the waste and reuse of resources, thus reducing maintenance costs. Moreover, the optimization model can make intelligent maintenance decisions based on the wind turbine’s maintenance history data and the magnitude of wind power. It can record the maintenance records of the wind turbine and then develop a more reasonable maintenance plan by detecting the wind power changes. In contrast, the maintenance plan under manual scheduling is usually based on experience and subjective judgment, so it lacks science and accuracy. It often only considers some factors, so it cannot optimize the maintenance work comprehensively. At the same time, the maintenance plan under manual scheduling cannot take into account the maintenance needs of the wind turbine in a timely manner, which leads to untimely maintenance work, increased downtime losses, and reduced power generation efficiency. In summary, by taking into account the maintenance cycle of wind turbines and wind size, the optimization model is able to reasonably arrange the time and sequence of maintenance tasks according to the actual needs and conditions, thus reducing maintenance costs and improving the efficiency of resource utilization. Therefore, the application of the optimization model in preventive maintenance is of great significance and value.

4.3. Sensitive Analysis

To further analyze the significance of wind prediction and optimization models for the management of offshore wind farms, four key parameters, namely, penalty cost per unit of wind loss, PM cost of a wind turbine, operating cost of a single service by a vessel, and maximum number of wind turbines maintained by a vessel at the same time, are selected for sensitivity analysis in this paper. Parameter configuration A is set for each algorithm, and 10 sets of data experiments are conducted using actual wind under different time intervals.

4.3.1. Impact of Parameter $p$

The effect of parameter $p$ on the total maintenance cost is shown in Figure 8. Increasing the penalty cost per unit of wind loss by the same amount will directly lead to an increase in the cost of wind loss during the maintenance of offshore wind farms, which in turn leads to an increase in the total maintenance cost. This is because during the PM of an offshore wind farm, the manager is responsible for the downtime losses due to the failure of the wind turbines to produce electricity during the maintenance period. The increasing penalty cost per unit of wind loss during this period will make the optimization model more inclined to schedule the optimal maintenance plan during the less windy time period to reduce the downtime loss and increase the wind turbine’s power generation efficiency. Consequently, managers must consider the influence of wind loss on maintenance costs during the formulation of maintenance programs. Simultaneously, proactive measures need implementation to mitigate penalty costs linked to wind losses, thereby lowering maintenance expenses and enhancing the economic efficiency and reliability of the system.

4.3.2. Impact of Parameters $u$ and $v$

Figure 9 and Figure 10 show the effect of parameter $u$ and parameter $v$ on the total maintenance cost, respectively. The figures clearly illustrate that an increase in the PM cost for a single wind turbine corresponds to a proportional increase in the maintenance cost for all wind turbines. This is because the PM cost includes the cost of the regular inspection, repair, and replacement of parts for the wind turbine, and the increase in these costs will directly affect the rise of the total maintenance cost. The optimization model will then develop the maintenance schedule in such a way that the time interval between each maintenance for each wind turbine will be as long as possible, so that it will be close to the maximum time interval between two adjacent maintenance sessions, thus reducing the number of maintenance visits to the wind turbines. There is also the potential to reduce the operating costs of the maintenance vessel to minimize the impact of increased PM costs on the total maintenance costs. In addition, similar to PM costs, total maintenance costs are also affected to some extent when the operating cost of a vessel for a single service increases. This is because an increase in the operating cost of a vessel means that more human, material, and financial resources are required to ensure the proper operation and maintenance of the vessel. When the operating cost of the vessel increases, the optimization model will increase the time interval between two starts of the vessel as much as possible and send as few vessels as possible to complete the maintenance tasks, so as to reduce the impact of the increase in the operating cost of the vessel on the total maintenance cost. At the same time, vessels performing maintenance tasks in offshore wind farms will make full use of the resources available to the maintenance vessel and try to have all maintenance personnel working together. This may result in higher maintenance costs for the wind turbines, as some wind turbines will be maintained more than once.

It can also be seen that the PM cost of a single wind turbine causes a more significant impact on the maintenance cost compared to the operating cost of a single service of a vessel. This is because offshore wind farms usually consist of dozens or even hundreds of wind turbines, and therefore managers need to carry out regular maintenance and servicing work on these wind turbines. These tasks include inspections, cleaning, lubrication, and replacement of parts to ensure proper operation and extend the life of the wind turbines. However, due to the large number of turbines and their wide distribution, these maintenance tasks require a large amount of human, material, and financial resources. As a result, PM costs for wind turbines account for a large proportion of the overall maintenance costs. In contrast, for maintenance vessels, managers usually only need to focus on the maintenance of individual vessels. And the operating cost of the vessel only occurs when cyclical preventive maintenance is required, so the operating cost of the vessel has a relatively small impact on the maintenance cost. Therefore, managers need to focus on the PM costs of wind turbines when developing maintenance programs and develop appropriate strategies and measures to reduce their impact. It is also important to rationally control and manage the vessel’s operating costs to ensure the economy and sustainability of the whole system.

4.3.3. Impact of Parameter $m$

In offshore wind farms, the maximum number of wind turbines to be maintained simultaneously by one vessel has a significant impact on the manager’s development of a maintenance program as well as maintenance costs. Examining Figure 11, it is evident that when the maximum number of wind turbines to be concurrently maintained by a vessel is fewer than the total number of wind turbines in an offshore wind farm, the overall maintenance cost rises with a decrease in the maximum number of wind turbines maintained simultaneously by the vessel. This is due to the fact that in this case, the vessel needs to take on more maintenance tasks and workload. When the maintenance capacity of one vessel is not sufficient to meet the needs of the offshore wind farm, the shipyard will need to send another vessel to fulfill the maintenance tasks, which results in an increase in the operating cost of the vessel and the maintenance cost of the wind turbines. When the maximum number of wind turbines to be maintained by one vessel is greater than or equal to the number of wind turbines in the offshore wind farm, the total maintenance cost does not change. This is because in this case, a single vessel will be able to fully utilize its maintenance capacity to efficiently complete the maintenance of all wind turbines in the offshore wind farm, thus maintaining a stable level of maintenance costs. Therefore, managers need to consider a number of factors when developing a maintenance program, including the number of vessels, the number of wind turbines each vessel can maintain, and the total number of wind turbines in offshore wind farms.

5. Discussions and Policy Implications

The prediction model based on deep learning methods and the optimization model based on mixed-integer programming methods work together well to minimize the maintenance-related costs of offshore wind farms under a random wind force. According to the numerical results in Section 4, the main managerial insights can be summarized as follows to support the scientific decisions of policy makers.

(1)

When establishing the maintenance planning for offshore wind farms, the accurate prediction of future wind force loss is crucial. There exists a substantial disparity between a solution derived from past data and the posterior optimal solution based on real data, often exceeding an average deviation of 30%. Hence, investing time and resources to enhance the precision of long-term wind forecasting is imperative.

(2)

When devising the maintenance plan for offshore wind farms, it is crucial to explore solutions offered by optimization models. This is due to the substantial disparity between a random solution and the optimal solution. Moreover, unlike manual planning incurring significant human resources and time, optimization models can swiftly and automatically provide appropriate solutions.

(3)

An optimal and efficient maintenance program not only minimizes resource wastage and energy loss but also upholds the principles of sustainable development. For instance, scheduling maintenance during periods of low wind is advisable to mitigate wind loss. Conversely, it is imperative to avoid scheduling maintenance during very high wind conditions as it poses risks to the safety of workers.

(4)

The variation in the values of different parameters leads to varying degrees of change in the maintenance-related costs of a wind farm. Considering that the operational and maintenance costs of a wind power plant directly influence its competitiveness in the market, owners of such facilities must determine an optimal plan based on their specific circumstances to minimize costs as much as possible.

6. Conclusions and Future Work

This study presents an optimization model for wind turbine maintenance planning, leveraging long-term wind speed predictions to enhance the cost-effectiveness of maintenance in offshore wind farms. In the wind speed prediction phase, a novel integrated wind speed prediction model denoted as VMD-CLSTM is introduced. This model employs variational mode decomposition (VMD) to partition raw data signals. Subsequently, a multilayer convolutional neural network (CNN) is utilized for feature extraction. A long short-term memory neural network (LSTM) is employed for the actual wind speed prediction. A mixed-integer linear programming model relying on wind speed data derived from VMD-CLSTM is formulated. The effectiveness of the wind forecast and the proposed model is demonstrated through multiple sets of experiments. Additionally, this paper conducts sensitivity analysis on key factors. The analysis can be used to examine the impact of changes in these factors on the deployment of maintenance plans and the total maintenance cost.

Future research can explore various aspects of the problem based on the results of this paper. For example, acquiring diverse sets of meteorological wind speed data from various regions is recommended. This will facilitate the establishment of correlations among data from different regions, enabling the joint training of prediction models and consequently enhancing prediction accuracy. Further exploration can be conducted into refining the maintenance strategy by organizing grouped maintenance and opportunistic maintenance policies for the multi-component wind turbine systems. This involves grouping turbines for collective planning and programming, contributing to a more systematic and efficient approach, which can be modeled by a Markov decision process and solved by the deep reinforcement learning methods.